In this study, we decomposed the broad practice of deciphering multiple solution strategies. We conducted interviews with 11 preservice elementary teachers, in which we asked teachers to decipher students’ standard and nonstandard strategies to multiplication and division problems. We examined what teachers said and did—what we refer to as “subpractices”—as they engaged in the broad practice of deciphering multiple strategies. Inductive analysis revealed the presence of 10 subpractices. The subpractice of comparing and contrasting nonstandard methods was associated with success in deciphering students’ strategies, whereas two other subpractices—identifying number decompositions and relating nonstandard methods to the standard algorithm—were at times associated with success but at other times with a lack thereof. This study adds to a growing body of work seeking to support preservice teachers in learning the complex practices of reform-oriented mathematics teaching by decomposing these practices into their component parts.

中文翻译：

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职前教师在解读学生多元解决方案时所说的和所做的

在这项研究中，我们分解了破译多种解决方案策略的广泛实践。我们对 11 名职前小学教师进行了访谈，其中我们要求教师解读学生对乘法和除法问题的标准和非标准策略。我们研究了老师所说的和所做的——我们称之为“子实践”——因为他们参与了解读多种策略的广泛实践。归纳分析揭示了 10 个子实践的存在。比较和对比非标准方法的子实践与成功解读学生的策略有关，而另外两个子实践——识别数字分解和将非标准方法与标准算法联系起来——有时与成功有关，但有时与成功有关。